N94- 29659 TDA ProgressReport42-116 February 15, 1994 The Rb 780-Nanometer Faraday Anomalous Dispersion Optical Filter: Theory and Experiment B. Yin, L. S. Alvarez, and T. M. Shay New Mexico State University, Las Cruces, New Mexico The Faraday anomalous dispersion optical filter may provide ultra-high back- ground noise rejection for free-space laser communications systems. The theoreticM model for the filter is reported. The experimental measurements and their com- parison with theoretical results are discussed. The results show that the filter can provide a 56-dB solar background noise rejection with about a 2-GHz transmission bandwidth and no image degradation. To further increase the background noise rejection, a composite Zeeman and Faraday anomalous dispersion opticM filter is designed and experimentally demonstrated. I. Introduction An important technical issue in free-space laser com- munications and remote sensing is to effectively reject the optical background while efficiently transmitting the sig- nal through the device. In general, an optical filter with high transmission, narrow bandwidth, wide field of view (FOV), and fast temporal response is needed to extract weak, narrow-bandwidth signals from strong, broadband background radiation, such as the ambient daytime solar illumination (Fig. 1). We have been exploring a new technology, the Fara- day anomalous dispersion optical filter (FADOF) [1 9], that provides a solution to this problem. The performance of the FADOF and other existing state-of-the-art narrow- bandwidth optical filters is summarized in Table 1. The noise rejection factor (NRF) is defined as NRF = 10 log 0 O<3 f T(A)_dA 0 (1) where T($) represents the filter transmission spectrum, dPnois_/d$ is the incident noise power spectrum, and _, is the signal wavelength. High NRF values of the filter mean high rejection for out-of-passband noise and high transmis- sion in the passband. The wide FOV and image-preserving characteristics make the filter useful for optical tracking in addition to optical communications. The interference filter 71 https://ntrs.nasa.gov/search.jsp?R=19940025156 2018-05-29T03:37:34+00:00Z
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N94- 29659
TDA ProgressReport42-116 February 15, 1994
The Rb 780-Nanometer Faraday Anomalous Dispersion
Optical Filter: Theory and Experiment
B. Yin, L. S. Alvarez, and T. M. Shay
New Mexico State University, Las Cruces, New Mexico
The Faraday anomalous dispersion optical filter may provide ultra-high back-
ground noise rejection for free-space laser communications systems. The theoreticM
model for the filter is reported. The experimental measurements and their com-
parison with theoretical results are discussed. The results show that the filter can
provide a 56-dB solar background noise rejection with about a 2-GHz transmission
bandwidth and no image degradation. To further increase the background noise
rejection, a composite Zeeman and Faraday anomalous dispersion opticM filter is
designed and experimentally demonstrated.
I. Introduction
An important technical issue in free-space laser com-
munications and remote sensing is to effectively reject the
optical background while efficiently transmitting the sig-nal through the device. In general, an optical filter with
high transmission, narrow bandwidth, wide field of view
(FOV), and fast temporal response is needed to extractweak, narrow-bandwidth signals from strong, broadband
background radiation, such as the ambient daytime solar
illumination (Fig. 1).
We have been exploring a new technology, the Fara-
day anomalous dispersion optical filter (FADOF) [1 9],
that provides a solution to this problem. The performanceof the FADOF and other existing state-of-the-art narrow-
bandwidth optical filters is summarized in Table 1. The
noise rejection factor (NRF) is defined as
NRF = 10 log0
O<3
f T(A)_dA0
(1)
where T($) represents the filter transmission spectrum,
dPnois_/d$ is the incident noise power spectrum, and _, is
the signal wavelength. High NRF values of the filter mean
high rejection for out-of-passband noise and high transmis-
sion in the passband. The wide FOV and image-preserving
characteristics make the filter useful for optical tracking inaddition to optical communications. The interference filter
where the prime denotes excited states, 7 represents per-
turbed states, /3 represents diagonalized energy states, Y
represents the eigenvector matrix for the Hamiltonian ma-trix H, and
ITFM) : _ YZ_M I/_FM) (7)
The reduced matrix element (J l[ d II J') is common to all
the hyperfine components of the spectral line and is given
by the relation
<J Itd IIJ'>"= (2J' + 1)hA3Ajs ' (s)
where A and A j j, are tile wavelength and transition prob-ability between levels J' and J, respectively.
Tile Rb 780-nm transition is between the ground state
52S1/2 and 52P3/2. Natural Rb has two isotopes with anabundance of 72-percent S_Rb and 28-percent S7Rb. The
magnetic energy levels of SSRb 5'P3/_ are shown in Fig. 4,and the spectrum of the relative transition intensities is
shown in Fig. 5.
The horizontal axis of Fig. 5 represents the transi-
tion frequencies, where 0 is the frequency (approximately
3.85 THz) corresponding to 780 nm. The two inside and
two outside byperfine transition groups are from the SSRband STRb isotopes, respectively. The relative intensity and
transition frequency of each hyperfine component depend
on the magnetic field.
The observed Zeeman spectrum depends on the viewingdirection and the polarization. In our calculations, we as-
sume that the incident radiation is linearly polarized trans-
verse to the magnetic field; therefore, the polarization can
be resolved into equal-amplitude left- and right-circularly
polarized components.
The Faraday rotation is a direct result of the difference
in the frequency dependence of the phase delay between
the right- and left-circularly polarized light. The Faraday
rotation angle ¢(w) is given by
_vL _¢(w) = %-c Re[n+(_) - fi_(w)]
wL= 5gc - (9)
where c is the speed of light, h+ and fi_ are the complex
refractive indices for the right- and left-circularly polar-
ized components, respectively, and n+ is the real part of
the complex refractive index fie. Taking into account the
contribution to the refractive indices from each hyperfine
component,
h±(w)= E h+(w,FM, F'M') (10)F,F_,M
73
If [fi+(w, FM, F'M') - 1] is much less than 1, the com-
plex refractive index for the circularly polarized light is
fie(w, FM, F'M') - 1 = CS+(FM, F'M')W(_vM,r,M,)
(11)
where S+(FM, F'M') is the line strength given in Eq. (4),
W(_FM,F'M') is the plasma dispersion function given by
1 f e -x_W(_rM,F'M') = _ =-- _FM,r'M'--OO
d= (12)
_ (w WFM,F,M, + i_)_FM,F'M' -- 7rAl]D
(13)
where the transition frequency between the levels FM and
F_M_wrM.F,M , is calculated from the eigenvalues of theHamiltonian, and
C -- 2rrN(F) (14)h(2J + 1)(2I + 1)AuD
where At] D is the Doppler width, and N(F), the popula-
tion density of the ground states hyperfine level F (assum-
ing the optical pumping is negligible), is given by
Ne-E(F)/KT
N(F) ._ _--_(2F + 1)e -E(F)/KT (15)F
where E(F) denotes the ground state hyperfine energy
level F, k is Boltzmann's constant, T is the cell tempera-ture in Kelvins, and N is the total rubidium ground-state
atomic number density.
The absorption coefficients of the atomic vapor are as-
sociated with the imaginary part of the complex refractive
index,
k,(_) = 2_Zm[_,(_)] (16)c
Therefore, the total attenuation of the linearly polarized
incident light intensity due to the absorbing medium is
74
a(w) = 0.5 (e -k+(_)L -t- e -L('°)L) (17)
With the crossed polarizers at the ends of the cell, thetransmission of the FADOF can be derived. As shown
in Fig. 6, the input polarized radiation Ei, can be decom-
posed into left-circular polarization, E+, and right-circularpolarization, E_. At the input of the cell, we have
Ein = EO&
E0 ^ E0 ^= -_-(x + i_)) + -_-(x - i_))
-- E+(0) + E_(0) (18)
After traveling through a FADOF cell of length L, thefields are
E+(L) = E+(0)exp[/_L]
EO ^
= T(_ + i_))
xexp[-_L+in+(_)WL] (19)
E_(L) = E_(0)exp[i_L]
E'o ^= -y(_ - i_)
x exp [-_--_ L + in-(--_)WL] (20)
The output field is
/_o,, = E+(L)_)+ E_(L)_)
• E0=,:
.Eo i_L] (21)_,:
L
K
=
w_
The FADOF transmission is given by
EE*
T(w)- E2°
= l{exp [-k+(w)L] +exp[-k_(w)L]
- 2c°s In+(w)- n-(W) wL ]c
×exp [ k+(w)+k-(W)L]}2
= - exp [-k+(w)L l + exp[-k_(w)L]4
-2c°s[2¢(w)]exp[-k+(w)+k-(W)L]}2 (22)
where ¢(w) is defined in Eq. (9).
In order to compare the FADOF with other types of
filters, we define the total equivalent noise bandwidth
(ENBW) for the FADOF as
oo
1 f T(w)dw (23)ENBW = T.,o----:-- 00
where T(w) represents the filter transmission spectrumand Tmax represents the maximum transmission for the
filter. The equivalent noise bandwidth corresponds to the
bandwidth of a rectangular notch filter with transmission
Tmax that transmits the same amount of noise as our fil-
ter. Using the equivalent noise bandwidth, we can eas-
ily compare different filter designs and even different filter
technologies.
Figure 7 shows the typical calculated spectrum of Rb
780-nm transmission at a temperature of 100 deg C and a
magnetic field of 90 G. The calculations include the con-tribution from both isotopes. The Rb FADOF shown has
an equivalent noise bandwidth of 4.7 GHz, a transmissionof 93 percent, and a signal bandwidth of 1.3 GHz.
III. Filter Transmission Spectra Measure-ments Compared With Theory
The FADOF was characterized using a tunable, narrow-
linewidth laser diode source. The tuning of a laser diode
is accomplished by varying the injection current or the
diode temperature. A single-mode 780-nm laser diode
(HL7802E) emitting 10 mW of optical power was used inour experiment. The laser diode current and temperature
were controlled by a custom-made diode laser controller.
The experimental setup is shown in Fig. 8.
A 12.5-cm-long solenoid coil generated the required
magnetic field. The magnetic field was controlled by vary-
ing the current through the solenoid. A flexible heater
strip was used to heat the Rb vapor cell. Two Glan-
Thompson polarizers with extinction ratios of 10 -5 served
as the polarizer-analyzer pair. The Rb vapor cell (2.5-
cm long) consisted of a small amount of Rb metal in anevacuated cell. Two PIN detectors, located as shown in
Fig. 8, were used to simultaneously measure the transmis-
sion spectrum of the Rb cell and of the FADOF.
A small triangle-waveform current ramp was superim-
posed on the laser diode's direct current to sweep the laser
emission wavelength across the FADOF transmission spec-
trum. Knowledge of the Rb hyperfine absorption spectralfeatures allowed the absolute wavelength calibration from
the frequency (energy) differences between the absorption
peaks of a Rb cell. A typical measurement of the Rb ab-
sorption spectrum is shown in Fig. 9.
The FADOF transmission spectrum was calibrated
against the measured absorption of the Rb cell. Figure 10
gives the results of such a comparison.
The absolute FADOF transmission was measured by
tuning the diode laser frequency to the center frequency of
the transmission peak and then measuring both the power
transmitted through, and the power incident upon, theFADOF. The ratio of these power measurements provided
the absolute FADOF peak transmission. The experimental
results were directly compared to the theoretical calcula-
tions after correcting for Fresnel reflection losses.
The Rb 780-nm FADOF transmission spectra are
shown in Fig. 11 for different combinations of B-field andtemperature. The solid lines in the figures are the mea-
sured spectra, and the dashed lines are the theoretical cal-
culations. The spectra show good agreement between the-
ory and experiment for all aspects of the filter, bandwidth,
75
peak transmission, peak center frequency, and spectral re-
sponse. The theory also predicts the observed 2-Gttz tun-
ability of the center frequencies and bandwidths of the
FADOF transmission peaks with applied magnetic fields
and cell temperatures.
IV. FADOF Imaging and Solar NoiseRejection Measurements
An important advantage of the FADOF over atomic
resonance filters is that the FADOF preserves the spatial
direction of the signal while filtering out the background
noise, but the atomic resonance filter does not [23]. For
free-space laser communications applications, this can be
used to advantage in the signal acquisition and tracking
system. We measured the spatial resolution of the optical
system to evaluate its applicability to a signal acquisition
and tracking subsystem. A schematic block diagram of the
imaging experiment system is shown in Fig. 12.
The target was illuminated by a 3-mW, 780-nm laserdiode. A small fraction of the scattered laser light wasthen incident on both the reference camera and the fil-
tered camera. This system allowed direct comparison of
the resolution of images recorded using the unfiltered and
filtered cameras. The advantages of the FADOF were
demonstrated by comparing the two images as the back-
ground light level was changed. The image resolution ex-
periments were performed with the room lights off and
using an imaging evaluation test target (Air Force MT-
1I). The resolution of both cameras was measured to be
170 #tad. Within the 170-/_rad resolution limit of our cam-era, no image degradation resulting from the insertion of
the FADOF was observed. Equipment with greater spatialresolution will be needed to measure the resolution limit
of the FADOF.
Figure 13 illustrates both the spatial resolution and thebackground rejection of the FADOF. The solar background
rejection was measured at 56 dB. The figure is a photo-
graph of the New Mexico State University (NMSU) logo
illuminated by a 3-mW laser diode and a cigarette lighter.
Also included in this photograph are the images from boththe filtered and unfiltered camera monitors. The unfil-
tered camera image (upper right) is clearly saturated bythe flame of the lighter, while the filtered camera image
(lower right) is unaffected by the flame. In addition, theletters "MEX" that are lost in the unfiltered camera im-
age due to the saturation are clearly visible in the filtered
camera image. The images were taken with approximately
76
2-nW/cm 2 of optical power incident on the charge-coupled
device (CCD).
VoThe Composite Zeeman/FADOF System
The transmission peaks of the FADOF are at the wings
of the absorption bands of the atomic vapor. For typi-
cal Rb and cesium (Cs) FADOFs, there are four transmis-
sion peaks caused by isotopic and hyperfine splitting. Nar-rowband laser signals are transmitted in one transmission
band, and light leakage through the other bands consti-
tutes a source of background noise and adds to the filter's
equivalent noise bandwidth. A composite filter system canisolate a single signal transmission band and eliminate theother transmission bands.
In the composite system, a Zeeman absorption cell is
placed in series with a FADOF. The Zeeman absorptioncell is tuned to absorb three of the four FADOF transmis-
sion bands. Optimal operating conditions for the absorp-
tion cell were found by calculating the absorption spectra
for different combinations of magnetic field and tempera-ture and matching these to the FADOF transmissions.
For right- and left-circularly polarized input, the ab-
sorption cell transmission is given as
a+ (w) = exp [-k+ (w)L] (24)
where "+" denotes the right- and "-" denotes the left-
circular polarization, k is the absorption coefficient, and L
is the cell length. The total transmission of the compositesystem is
T(w) = TFADOF(W)a+ (w) (25)
where TFADOF(a/) is the transmission spectrum of theFADOF.
The block diagram of the composite system for a Rb
780-nm FADOF is shown in Fig. 14. A quarter-wave plateis used to transform the linearly polarized FADOF output
to right- or left-circularly polarized input for the absorp-tion cell.
Figure 15 shows the Rb 780-nm FADOF transmission
curve at a magnetic field of 60 G and a temperature of
90 deg C. The four transmission peaks of average band-width at approximately 0.7 GHz each are characteristic of
_E
thisFADOFundertheseconditions.Calculationsshowedthat theabsorptionof a Rb Zeemancellat 100degCin a 1300-G B-field could be tuned to match the FADOF
transmission peaks and results in a single-peak transmis-
sion spectrum.
Figure 16 shows the agreement between the theoretical
and experimental absorption curves for right-circularly po-
larized light incident on the Rb Zeeman cell. The resulting
composite filter transmission is shown in Fig. 17.
The single-band transmission spectrum in Fig. i7 was
obtained by tuning the system so that the right-circularly
polarized absorption band of the Zeeman absorption cell
overlapped three of the four transmission peaks in theFADOF transmission spectrum and left the transmission
of a single peak unchanged. By cascading the filters in this
way, the ENBW was reduced by a factor of 3.5, from 3.0to 0.86 GHz.
With the end application of the filter in mind, we com-
pared the bandwidth of the composite filter to that of aFourier-transform-limited Gaussian pulse. This is shown
in Fig. 18, where it is seen that a transformed 5-nsec Gaus-
sian pulse just fits under the envelope of the filter. Pulse
position modulation is the preferred modulation format
for deep space optical communications; this experimentshows that the composite filter can provide good back-
ground rejection for detection of 5-nsec-wide laser pulsesat the optical communications receiver.
Vl. Summary
The FADOF has been shown to be able to provide
high background noise rejection, high throughput, fast
response, and a wide field of view while preserving im-
age information. The general theory for the FADOF was
presented in this article. It predicts the FADOF perfor-
mance for arbitrary magnetic fields and temperatures of
the atomic vapors with and without hyperfine structure
components. The theory was used to predict the transmis-sion spectrum and performance of a 780-nm Rb FADOF,
based on the solved quantum mechanics equations for the
atomic levels and transition line strengths for tile Rb va-
por. The experimental results show very good agreement
with theoretical predictions.
A composite Zeeman FADOF filter has been described
and shown to be compatible with a Fourier-transform-
limited 5-nsec laser pulse. The filter pair exhibits a singleultra-narrow passband in the transmission spectrum and is
expected to reduce the noise rejection factor of the FADOF
by 3.5.
Acknowledgments
The authors wish to thank J. Lesh and K. Wilson in tile JPL Optical Com-
munications Group for many helpful discussions and suggestions. Thanks are also
expressed to D. C. Yuan and Q. C. Liu for their assistance.
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79
Table 1. The performance of some narrow bandwidth optical filters.